The concept of device equivalence is introduced. In equivalent devices, the light propagation can be described by identically evolving modal expansions, resulting in identical power transfer ratios. By first applying this concept to a z-invariant structure with a low refractive-index contrast it is shown how a normalized coordinate space can be defined in which equivalent structures have exactly the same geometry. Subsequently it is shown how this normalized coordinate space can be defined for z-variant integrated optical devices, again provided that the lateral refractive-index contrast is small. This normalization makes it possible to perform numerical device simulations in normalized coordinate space, the results being applicable to a large set of equivalent devices. Furthermore, starting from a known design, it simplifies redesigning that device for use at another wavelength or using other materials significantly, the resulting device being equivalent to the original one